I teach a geometry/algebra course for middle school teachers at our local university. I did not develop the course, hence I use materials collected from other professors. I generally follow the homework schedule and assignments of other profs. I fielded a question from one of my students about a homework problem I felt comfortable dealing with, but for which I had not quite worked out all the details. There was a very obvious triangular number pattern, for which I know, on a good day, a general approach to identify the pattern based on consecutive digits. This problem's pattern had a (x-1)(x-2)÷2 pattern, which I saw, but could not quite identify and I was left staring at the board. After some time, I turned to the class and told them that while I could see the pattern, I could not name it.
I don't know why I drew such a terrible blank. I felt guilty not having the answer, but worse than that, I felt that I let them down with my lack of finesse in that moment.
I am a good teacher, sometimes a great one, and still there are times when I come a big ZERO, even on problems I should and often do know.
Has that ever happened to you?